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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.18261 |
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Table of Contents:
- Let $Σ_{g,*}$ be a once-punctured oriented surface of genus $g$. We study the action of the mapping class group $Γ_{g,*}$ on the $n^{th}$ rational cohomology of the configuration space $\text{Conf}_n(Σ_{g,*})$ of injections $\{1,\ldots, n\}\hookrightarrow Σ_{g,*}$, and compare the kernel $J_{g,*}^{cfg}(n)$ of this action with the $n^{th}$ Johnson subgroup $J_{g,*}(n)$. We find high-rank abelian subgroups in the quotient $J_{g,*}^{cfg}(n)/J_{g,*}(n)$ arising from the higher Johnson images and from symplectic representation theory. In particular we refute a conjecture due to Bianchi--Miller--Wilson.